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arXiv · 1011.1777

Bak--Sneppen type models and rank-driven processes

Michael Grinfeld·Philip A. Knight·Andrew R. Wade
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Abstract

The Bak--Sneppen model is a simple stochastic model of evolution that exhibits self-organized criticality and for which few analytical results have been established. In the original Bak-Sneppen model and many subsequent variants, interactions among the evolving species are tied to a specified topology. We report a surprising connection between Bak-Sneppen type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behaviour of the fitness profile in the anisotropic Bak--Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously.

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Michael Grinfeld, Philip A. Knight, Andrew R. Wade. 2010-12-03. Bak--Sneppen type models and rank-driven processes. https://doi.org/10.1103/physreve.84.041124

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